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Rapp says he managed to "squirm" away from the actor, who would have been aged 26 at the time.

Last night, double Oscar winner, 58, issued a stunning statement in which he said he did not remember the encounter, but offered "the sincerest apology".

The American Beauty and Usual Suspects star also said the story had prompted him to confirm he has had relationships with both men and women in his life, but now lives "as a gay man."

The statement, posted on Spacey's Twitter account, read: "I have a lot of respect and admiration for Anthony Rapp as an actor.

"I'm beyond horrified to hear his story.

"I honestly do not remember the encounter, it would have been over 30 years ago.

"But if I did behave as he describes, then I owe him the sincerest apology for what would have been deeply inappropriate drunken behaviour, and I am sorry for the feelings he describes having carried with him all these years.

"This story has encouraged me to address other things about my life.

"I know that there are stories out there about me and that some have been fuelled by the fact that I have been so protective of my privacy.

"As those closest to me know, in my life I have had relationships with both men and women. I have loved and had romantic encounters with men throughout my life, and I choose now to live as a gay man.

"I want to deal with this honestly and openly and that starts with examining my own behaviour."

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In an interview with Buzzfeed News, Star Trek star Rapp said he attended a party on his own in 1986 after befriending Spacey and was the only non-adult there.

Becoming bored, Rapp went into a bedroom and watched TV until after midnight, when he realised no one else was left in the apartment.

At that point, Rapp alleges that Spacey entered the bedroom, picked him up, and climbed on top of him in a sexual advance.

Spacey, who moved to London and was artistic director of the Old Vic theatre for 10 years, would have been 26 at the time.

"My memory was that I thought, 'Oh, everybody's gone.

"Well, yeah, I should probably go home'," Rapp said.

"I have a lot of respect and admiration for Anthony Rapp as an actor.

He claimed that Spacey "sort of stood in the doorway, kind of swaying.

"My impression when he came in the room was that he was drunk."

Rather than saying anything, Rapp said Spacey "picked me up like a groom picks up the bride over the threshold.

"But I don't, like, squirm away initially, because I'm like, 'What's going on?' And then he lays down on top of me."

Rapp explained that he couldn't remember how long Spacey was on top of him, but after a short amount of time, he was able to "squirm" away.

Rapp said that he has not spoken with Spacey since the incident, but that he told the story to several friends and family over the years.

He said he was prompted by the Harvey Weinstein scandal to speak out, after watching numerous women come forward with allegations of their own.

"And not to simply air a grievance," he said, "but to try to shine another light on the decades of behavior that have been allowed to continue because many people, including myself, being silent. ... I'm feeling really awake to the moment that we're living in, and I'm hopeful that this can make a difference."

Kevin Spacey (Image: PA)

Rapp said he met Spacey for the first time at one of the celebratory events being held amid the success of "Precious Sons," which Rapp starred in, and "Long Day's Journey Into Night," which was Spacey's first breakout role.

Before the alleged incident at Spacey's apartment, Rapp described Spacey as having invited both him and a 17-year-old friend to a nightclub, Limelight, after meeting them at a second post-show celebration.

Rapp said Spacey invited them to the club despite the fact that Rapp "looked younger than 14."

Rapp does not recall Spacey offering them any alcohol, and he remembers the night as "a fun night of talking and hanging out."

"I came forward with my story, standing on the shoulders of the many courageous women and men who have been speaking out, to shine a light and hopefully make a difference, as they have done for me," Rapp said in a statement to Variety.

"Everything I wanted to say about my experience is in that article, and I have no further comment about it at this time."

In a glittering career, Spacey has starred in a number of dark Hollywood thrillers such as LA Confidential and Seven.

He elevated his icon status in recent years with his award-winning role as US President Frank Underwood in the Netflix drama 'House of Cards.'